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 A010030 Irregular triangle read by rows: T(n,k) (n >= 1, 0 <= k <= [n/2]) =  number of permutations of 1..n with [n/2]-k runs of consecutive pairs up and down (divided by 2). 3
 1, 1, 0, 3, 0, 3, 8, 1, 25, 28, 7, 17, 155, 143, 45, 259, 1005, 933, 323, 131, 2770, 7488, 7150, 2621, 3177, 27978, 64164, 62310, 23811, 1281, 51433, 294602, 619986, 607445, 239653 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 REFERENCES F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied Tables, Cambridge, 1966, p. 264. LINKS FORMULA G.f. for number of permutations of 1..n by number of runs of consecutive pairs up and down is Sum(n!*(((1-y)*(2*x^2-x^3)-x)/((1-y)*x^2-1))^n,n = 0 .. infinity), cf. A010029. - Vladeta Jovovic, Nov 23 2007 EXAMPLE Triangle begins: 1, 1, 0, 3, 0, 3, 8, 1, 25, 28, 7, 17, 155, 143, 45, 259, 1005, 933, 323, 131, 2770, 7488, 7150, 2621, 3177, 27978, 64164, 62310, 23811, 1281, 51433, 294602, 619986, 607445, 239653, ... CROSSREFS Cf. A002464, A001266, A000239, A000544, A001282. Sequence in context: A021771 A154853 A139214 * A197270 A117940 A099093 Adjacent sequences:  A010027 A010028 A010029 * A010031 A010032 A010033 KEYWORD tabf,nonn AUTHOR EXTENSIONS More terms from Vladeta Jovovic, Nov 23 2007 Entry revised by N. J. A. Sloane, Apr 14 2014 STATUS approved

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Last modified June 21 02:50 EDT 2021. Contains 345351 sequences. (Running on oeis4.)